Economic attractiveness of domestic rainwater harvesting in Brazilian cities

Brazil is the fifth largest country by area in the world, with a variety of climates in its territory. This work assesses the economic attractiveness of domestic rainwater harvesting direct feed systems, for the replacement of non-drinking water, in 148 locations of the Brazilian territory considering hourly rainfall data for the 14-year period between 2008 and 2021. The water tariff and consumption data for each location were also considered along with estimated hourly and monthly consumption patterns. With annual operating expenses at 1% of the capital expenditure and an annual discount rate of 8%, the net present value for the 14-year period is positive in only 15 locations, which are among those with the highest water tariffs in the country. The results of these base case simulations discourage the installation of domestic RWH systems in most of the Brazilian locations considered. However, the results also show that, depending on house occupancy, filtration equipment cost, water tariff, and catchment area, outcomes more favorable to the installation of RWH systems are obtained, especially in cities of Brazil’s southern and southeastern regions.


Introduction
Domestic rainwater harvesting (RWH) systems reduce water consumption from public suppliers, especially for those uses that do not require drinking water [1]. They can also contribute to minimizing floods and torrents during heavy rain episodes, as demonstrated by studies in different parts of the world [2][3][4][5][6], and serve as a water reserve for when an interruption of the public water supply occurs. There are several types of incentives to install them: climatic, as in the case of remote arid and semi-arid regions [7]; legal, because of laws that impose their installation [8]; and economic, either because of their intrinsic performance or because of subsidies. In the absence of a legal obligation, the installation of a 1 3

Rainfall data
Historical rainfall data were obtained from the Brazilian National Institute of Meteorology (Instituto Nacional de Meteorologia-INMET) [26]. At the time of the writing, it contains hourly rainfall data between 2000 and 2021 for a growing number of Brazilian cities. As observed previously [25], there are gaps in the data.
To strike a balance between the number of measurement sites and the length of the data series, we used data for a period of 14 years between 2008 and 2021. In most cases, each location corresponds to one city, with exception of Rio de Janeiro, RJ, which has data for three measurement sites.

Criteria for city selection
If, in the data set for a given city and year, the missing data amounted to less than 20% of the expected number of rainfall measurements-one every hour-the missing data were assumed to be 0 mm of rain during that hour, following a procedure adopted before [25] for the same database. Above the 20% threshold, the data set for that year was discarded and, in the economic evaluation, the result for the following year was repeated. All the locations with more than three failed yearly data sets were discarded. Only locations with an acceptable data set for the first year of the series (2008) were included. This screening process ended with a list of 148 locations ( Table 2).

Water consumption and tariff data
The average daily water consumption per person and the water tariff, in Brazilian reais, were obtained for each city in the year 2020 (the most recent data available) from the National System for Sanitation Information (Sistema Nacional de Informações sobre Saneamento) [27]. These tariffs were converted from Brazilian reais to United States dollars using the average exchange rate for 2020, which was taken as US$ 1.00 = R$ 5.156. These tariffs were considered as flat rates per cubic meter because there is no information about basic charges and consumption tiers in the database [27].
To calculate the water consumption per household, the number of occupants is necessary. The most recent official information, from the 2010 census [28], is that the average number of occupants in a Brazilian household is equal to 3.31.
Roof-harvested rain water, if untreated, may pose biological and chemical risks. For example, a study from Australia [29] shows that pathogens, likely from fecal materials of small animals with access to the roof, may be present in harvested rainwater. It suggests, for the sake of prudence, water boiling, UV or other forms of disinfection prior to use as potable water. A study from South Africa [30] mentions that the microbial quality of harvested rainwater may not always comply with drinking water standards. Further, a recent publication [31] points out that the concentration of four perfluoroalkyl acids (PFAAs)-some of the so-called forever chemicals-in rainwater exceeds the United States Environmental Protection Agency Lifetime Drinking Water Health Advisory levels. Thus, the percentage of the total domestic use of water that can be replaced by harvested rain water will depend on whether the RWH facility will treat the water to make it suitable for human consumption and personal hygiene. The assumption adopted in this work is that the treatment will not reach such levels. Therefore, it was considered that the harvested rain water will not be used for activities such as showering, hand washing, dish washing, and food preparation. It was considered that the harvested rain water can be used in toilets, clothes washing, and other applications that require little water treatment. Such uses in Brazilian households range from 19 to 40% of the domestic water consumption according to a study [32] that compiled information from three different sources. According to literature information on domestic water use in the United States of America [33], such percentage is 43%, which is the value adopted for the calculations of this work.
We also accounted for the monthly and hourly water consumption patterns. Based on literature data [34], we define f M and f h as multipliers of the average hourly water consumption, which depend on the month and on the time of the day, respectively. The monthly multiplier f M embeds a six-month shift with respect to the original data, which is based on the northern hemisphere, because most Brazilian cities are in the southern hemisphere. Table 1 shows the values adopted.

Capital and operating expenses
The capital expenditure, I, in equipment was assumed to be equal to the summation of the costs of three units: a pump, a filter kit for RWH systems, and a polyethylene storage tank. These costs were obtained in Brazilian reais from local vendors and converted to US dollars using the exchange rate of the day. The cost of installing the RWH system was neglected.
The value of the annual operating expenses, OPEX, is calculated as a fraction f e of the capital expenditure:

Contingencies
In addition to its regular role as part of the RWH system, it is assumed that the tank can have the additional role of storing water for emergency uses when there is an interruption of the public water supply. To consider that, we specify V min as the minimum volume of water allowed in the tank during its normal operation.

Water balance in the tank
There are two main types of RWH systems: gravity feed systems, in which the harvested water is pumped to a header tank from where it flows by gravity when needed, and direct feed systems, in which the harvested water is pumped directly to the point of consumption. A review paper on energy intensity in RWH systems, with authors from Australia and Brazil [38], concludes that gravity feed systems have the potential to be more energy-efficient than direct feed systems. Other sources [39,40] present a different view and point out that, for maximum reuse of rainwater, direct feed systems tend to be more efficient. A recent study from Brazil [41] claims that direct feed systems are more energy-efficient but concluded that gravity and direct feed systems led to similar paybacks for RWH systems in the city of Maringá, in the State of Paraná.
Here, it is assumed that direct feed systems will be used. As we consider that the water density is constant, the mass balance of water in the tank is replaced by a volumetric balance. The initial volume of water inside the tank is V 0 . At the end of any subsequent time interval i, the volume of water in the tank, V i , is: The symbol ΔV i represents the change in volume of water in the tank during interval i. In these equations, H i represents the rainfall in during interval i, A is the roof catchment area, and D is its drainage coefficient [42], which is the fraction of the rainwater collected on the roof. The symbol ẇ h represents the average nondrinking water consumption per household per hour and Δt i is the time interval in the rainfall measurements, which is of one hour in this work. If V i < V min , V i is set to V min , with the water deficit covered by the public supplier. If V i is larger than the tank's capacity, V max , V i is set to V max , and at least part of the rainfall during interval i is not harvested. In this case, the volume harvested during interval i is: Therefore, (ΔV i ) in , calculated either with Eq. 4 or 6, is the volume of water harvested during interval i.

Performance indicators
To analyze the results, we use the harvest/demand ratio of non-drinking water and net present value of the RWH system. The calculations are based on historical rainfall data during a period of 14 years, between 2008 and 2021, to project the performance an RWH system would have during its operation. We neglect the effect of inflation and assume the investment is done in year 0, that is, in 2007.

Harvest/demand ratio of non-drinking water
The harvest/demand ratio of non-drinking water ( R HD ) is calculated dividing the volume of water harvested during a period of n p time intervals by the non-drinking water consumption during the same period: It is possible that R HD > 1 in a given period and this indicates that more water is harvested than utilized during the period. This water surplus stays in the tank for later use.

Net present value
The net present value (NPV) is calculated using: where n y is the number of years, r is the annual discount rate, and S j is the savings in year j, which is the difference between the savings in water bills and the operating expenses (Eq. 1): where n p,j is number of time intervals in year j and C is the water tariff in a given location. We use the symbol NPV 14 to represent the net present value for the 14-year period considered in this work.

Computational implementation
All the calculations described in this section were carried out using a program in Python, developed in-house, that takes advantage of parallelism to speed up its execution.

Results
This section is divided into subsections, the first of which presents base cases that disregard operating costs and discount rates. These are considered in subsequent subsections. Then, there are subsections about the effects of occupancy, filtration equipment cost, water tariffs, and catchment area.

Base cases
As of 2019, 85.6% of the permanent private households in Brazil were houses [43], with tile roofs used in 81.9% of them [44]. Based on these data, the model home adopted in this work is a house with tile roof. The average drainage coefficient calculated using the values and ranges reported in reference [45] is equal to 0.84. This value is in very good agreement with the value adopted in our calculations − 0.85-which is the mid-value of the interval [0.8, 0.9] for tile roofs according to Biswas and Mandal [46]. Using values smaller than 0.85 for the drainage coefficient would lead to a more conservative analysis because of the smaller fraction of the rainwater collected on the roof; using values larger than 0.85 would have the opposite effect. The average area of the 10% most expensive houses financed in Brazil was equal to 136 m 2 in 2021 [47]. This upper market tier probably has the most discretionary income to invest in the installation of an RWH system. To that area, we added 10% to account for the roof's eaves, obtaining a total catchment area of 150 m 2 , which is the value used in our base cases.
A household with 3.31 occupants is assumed. This is the average number of occupants according to Brazil's most recent census. The minimum and initial volumes of water in the tank are 10% and 50% of the tank's capacity, respectively. The operating expenses and the discount rate are both equal to zero. Figure 1, plotted using maps from the Brazilian Institute of Geography and Statistics [48] loaded into the QGIS geographic information system software version 3.26.2 [49], displays the NPV 14 . Points with lighter colors have small NPV 14 (negative in several cases) and those with more intense colors have large NPV 14 . Overall, there is a substantial scattering of the NPV 14 , depending on the location, which indicates a large disparity in the economic attractiveness of installing a domestic RWH system.
In Fig. 1, there are very few points in the northern part of the country, which mostly corresponds to the Amazon region. This results from the few rainfall data sets for this part of the country that passed our completeness tests for inclusion in this study. Most of the locations that passed these tests are in the northeastern, southeastern, southern regions, which have the largest population densities.
Another observable trend in Fig. 1 is that, for all tank capacities, the NPV 14 is small, and often negative, in the northeastern cities, despite the fact that some of them are in a semi-arid region. This is a consequence of low water consumption and low water tariffs. On the other hand, the southernmost state, Rio Grande do Sul (RS), has some of the largest NPV 14 because of the high water tariff in many of its cities, possibly because this affluent state occasionally undergoes periods of severe drought.
The number of times the [500, 1000, 2000, 5000, 10,000, 20,000] L tanks lead to the largest NPV 14 is respectively equal to [7,99,16,26,0,0]. Therefore, a 1000 L tank would be the most favorable solution in 66.9% of the 148 locations considered. The largest tanks, of 10,000 L and 20,000 L, are too costly for the conditions of this case study and never provided the best solution for any given location.
There are 58 locations where at least one tank capacity leads to a positive NPV 14 . Among them, the 1000 L tank gives the best solution 19 times, while the numbers of times for the 2000 L and 5000 L tanks are 14 and 25, respectively. Interestingly, among the 25 locations with the largest NPV 14 , the best solutions are achieved 6 times with the 2000 L tank and 19 times with the 5000 L tank. The general observation is that, for conditions that favor a positive NPV 14 , the best tank capacities tend to be either 2000 L or 5000 L, depending on the specific conditions of the location. To illustrate the results of our simulations, Fig. 2 shows the volume of water inside a 1000 L tank as a function of the day of the year in Brasília, which is Brazil's capital city and selected because its rainfall data set is quite complete. Based on the NPV 14 , the 1000 L tank is the best option in Brasília. In Fig. 2a, the solid line represents the average volume of water in the tank, which was calculated as follows: for each date and time, the hourly values for each of the 14 years were averaged. The values for 29 February in the leap years were discarded. The curve for the average is deceitful in the sense that it might give the impression that the tank never fills up during the year, but this is not correct. Figure 2a includes the results for 2020, which was chosen arbitrarily. Despite the effects of the COVID-19 pandemic during 2020, official data [50] show that the per capita water consumption for that year in the Brasília region was within 0.2% of the average for the period 2017-2020. The results for 2020 show that the tank fills up and empties to the minimum acceptable volume of 100 L several times during the year. Figure 2b shows the standard deviations, which are quite large, with exception of a period of about 50 days in the middle of the year, when Brasília is notoriously dry. During this period, it is almost certain that the water in the tank will be at its minimum acceptable level.
Next, results for the cities of Belém, in the State of Pará (PA), and of Frederico Westphalen, in the State of Rio Grande do Sul (RS), are compared. The choice of these two cities, which are about 3500 km apart, is arbitrary but they have several contrasting factors. Belém is in the northern region and is the rainiest state capital in Brazil. Frederico Westphalen is located in the southernmost, drought-prone Brazilian state, where water tariffs are high. Unlike Belém, Frederico Westphalen ranked among the most favorable locations for the installation of an RWH system according to our calculations. Fig. 3 compares the harvest/demand ratio of non-drinking water for the case of a city with a tank of 1000 L (Belém, in the State of Pará (PA)) and another with a tank of 5000 L (Frederico Westphalen, in the State of Rio Grande do Sul (RS)). These capacities are the most favorable for these cities based on the NPV 14 . The average R HD for the whole period is 0.947 in Belém and 0.954 in Frederico Westphalen, that is, about 95% of the non-drinking water demand is fulfilled by the harvested rainwater. Figure 3 also shows that the fluctuation in R HD is larger in Frederico Westphalen than in Belém. In the former, because of the larger tank capacity, the harvested volume may be much more than the demand in rainy months and, in dry months, the harvested volume may be much less than the demand. To analyze this difference, it is useful to observe the average monthly rainfalls, which are compared in Fig. 4. During the period considered, the average annual rainfall was 3334 mm in Belém and 1906 mm in Frederico Westphalen. With a smaller water demand per occupant and plenty of rain, the best tank capacity for an RWH system in Belém is 1000 L, which supplies 95% of the non-drinking water needs. With less rain and a higher water demand per occupant, an RWH system in Frederico Westphalen needs a larger tank to fulfill the same percentage of the local demand. Figure 5 shows the the harvest/demand ratio of non-drinking water in the city of Frederico Westphalen for the tank capacities of 2000 L, 5000 L, and 10,000 L, whose average R HD for the whole period are 0.819, 0.954, and 0.996, respectively. There are periods when the curves for the 5000 L and 10,000 L tanks overlap-and even some periods when all three curves overlap-during which the tank capacity is not the limiting factor for RWH. As the tank capacity increases, the peaks in the harvest/demand ratio become more pronounced because more water can be stored during rainy periods. The largest average harvest/demand ratio, R HD = 0.996 , is for 10,000 L tank but its NPV 14 is less than that for the 5000 L tank, whose average harvest/demand ratio is R HD = 0.954.

Accounting for operating expenses
Next, we consider the effect of the operating expenses. As this decreases the NPV 14 , this calculation was done only for the 58 locations that had positive NPV 14 in the previous subsection. It is assumed that the annual operating expenses are 1% of the capital expenditure. Figure 6 shows the results, with the 41 locations where RWH systems would have positive NPV 14 . Remarkably, no city of the northern and northeastern regions appears and most cities are in the southernmost state of Rio Grande do Sul. A tank with capacity of 1000 L is the best option in 9 of these locations, 2000 L is the best tank in 11 locations, and 5000 L is the best option in 21 locations.

Accounting for discount rates
For the 41 locations with positive NPV 14 when the operating expenses are 1% of the capital expenditure, we also consider the effect of the discount rate for tanks with capacities of 1000 L, 2000 L, and 5000 L.
As an example, Fig. 7 shows the net present value in the city of Frederico Westphalen as a function of the number of years after the startup of the RWH system for different values of the discount rate. In all cases, the NPV for 14 years of operation is positive and the payback period is in the interval [6,9] years, depending on the discount rate. The best tank capacity also depends on the discount rate. For the discount rates of 0%, 2%, and 4%, the best tank capacity is 5000 L and the project value at startup is equal to (-US$ 1001.72). For the discount rates of 6% and 8%, the 2000 L is better and the project value at startup is equal to (-US$ 790.96). Figure 8 displays analogous results for the city of Alto Paraíso de Goiás, GO. With 0% discount rate, the best tank capacity is 5000 L but, for the other  14 . For the discount rates of 0%, 2%, and 4%, the NPV 14 is positive but it is negative for the 6% and 8% discount rates. For both locations, increasing the discount rate favors the downsizing of the RWH system. In fact, this is a general trend, as shown in Fig. 9. It displays the number of cases in which  Based on these results for this sample of 148 locations, a 150 m 2 roof area, the Brazilian average of 3.31 occupants, and additional assumptions of these base case simulations, a house owner would typically have economic incentive to install an RWH system in few Brazilian cities. Under such scenario, the decision to install an RWH system would result from considering additional factors, such as water security and the perception of contributing to community efforts to reduce the impact of floods and water torrents. The cities with the most favorable conditions for domestic RWH are generally located in the southernmost State of Rio Grande do Sul, which is an interesting outcome because this state is prone to suffer periods of drought. Despite the use of different indicators, this result agrees with literature findings [25] that point at Porto Alegre, the state's capital city, as having the greatest potential for RWH among four other Brazilian

Effect of occupancy
The domestic water consumption is calculated in this work multiplying the number of occupants by the location-dependent per capita consumption [27], and then assuming that a fraction (43%) of this consumption can be replaced by harvest rainwater. Therefore, studying the effect of occupancy is tantamount to studying the effect of water consumption. We simulated cases with ± 1 and ± 2 occupants from the national average value of 3.31. With the specifications given in its caption, Fig. 11 shows the effect of the average occupancy on the number of locations with positive NPV 14 . With more occupants, the domestic water consumption grows, increasing the number of locations that benefit from the installation of RWH systems. This observation is aligned with literature results [51] indicating that the number of occupants is correlated with tendency to adopt domestic RWH systems.

Effect of the filtration equipment cost
The base case calculations were done using the cost of off-the-shelf equipment, readily available from major suppliers in the Brazilian market. It might be possible to reduce the cost of equipment by using filtration systems developed onsite at a fraction of the kit price. For the set of specifications informed in its caption, Fig. 12 shows

Effect of water tariffs
Water tariffs are based on consumption tiers in many cities. While it is relatively simple to account for such tiers at a single location (e.g., [52]), price policies are city-dependent and this is information is unavailable in the public database [27] used as data source in this work, which only reports the base tariff. Here, we multiply this base tariff at each location by a water tariff multiplier. A multiplier equal to 2 means that the average water tariff is twice the base tariff listed in the National System for Sanitation Information [27]. We simulate the RWH system for different water tariffs, with the fixed values of the other variables shown in the caption of Fig. 13, which displays the effect of the water tariff multiplier on the number of locations with positive NPV 14 . The number of locations with positive NPV 14 is rather sensitive to the average water tariff. For instance, this number of locations nearly quadruples when the water tariff multiplier changes from 1 to 2, changing from 14.2 to 53.4% of the 148 locations analyzed in this work. These locations belong to 11 states, mostly in the southern and southeastern regions, and to the Federal District (Brasília region). The importance of water tariffs on attractiveness identified here is aligned with previous observations of our own group regarding the city of Asunción, in Paraguay [52].

Effect of catchment area
In 2021, the average area of the houses financed in Brazil was 66 m 2 [47], to which we added 10% to account for the roof's eaves. This results in a catchment area of 72.6 m 2 , which was rounded to 75 m 2 . In this way, this catchment area is half of the base case area of 150 m 2 . Figure 14 compares the number of locations with a positive NPV 14 for roofs with catchment areas of 75 m 2 and 150 m 2 , for various water tank capacities. The additional specifications to run these cases can be found in the caption of Fig. 14.
For the 20,000 L tank, none of the two catchment areas considered gives a location with positive NPV 14 . For the other tank capacities, the catchment area of 150 m 2 leads to more locations with positive NPV 14 than the 75 m 2 catchment area. As the 75 m 2 catchment area is representative of the average house financed in Brazil in 2021 [47], this result suggests the economic attractiveness of domestic RWH systems will depend on favorable conditions related to occupancy, equipment cost, and water tariffs. Finally, it is also observed that cities of the state of Rio Grande do Sul are the most common among the locations with positive NPV 14 in Fig. 14.

Conclusions
This work presented an economic assessment of rainwater harvesting for domestic applications in 148 Brazilian locations using historical rainfall data for the 14-year period 2008-2021, official statistical data for water consumption and tariff in each of these locations, and current equipment prices to assemble rainwater harvesting systems in Brazil. It is important to stress that the results reported in this paper only considered the economics of RWH systems from the perspective of a house owner. In households with 150 m 2 and 3.31 occupants, even disregarding operating expenses and discount rates, only 58 locations, or about 39.2% of the total, had positive net present values for this 14-year period. When annual operating expenses equal to 1% of the capital expenditure were considered, the number of cities with positive net present values for this 14-year period dropped to 41, or about 27.7% of the total. When discount rates were also taken into account, the number of locations with positive net present values for this 14-year period dropped further: only 15 locations, about 10% of the total, when an annual discount rate of 8% was applied. In terms of geography, although many cities in the Brazilian northeast are in a semi-arid region, our base calculations suggest that the economic attractiveness of installing RWH systems there is low because of the little rainfall, small water consumption, and low water tariff. On the other hand, also according to our base case calculations, Brazil's southernmost state of Rio Grande do Sul exhibits the most favorable conditions for the installation of RWH systems, as a result of the high water tariffs in its cities, compared to those in cities of other states.
This study also demonstrated that, compared to the base cases, higher occupancies, lower filtration equipment costs, larger water tariffs, and larger catchment areas affect the net present value for the 14-year period considered, generating scenarios that are favorable to the installation of domestic RWH systems in more locations in Brazil, particularly in cities of the southern and southeastern regions.